Algebra and Dynamics
Math 275 - Tu Th 10:00-11:30 pm - 209 Science Ctr
Harvard University - Spring 2003
maps on projective space and algebraic surfaces, Coxeter groups, flows on homogeneous spaces and polygonal billiards.
Instructor:
Curtis T McMullen
Texts
- J. E. Fornaess, Dynamics in Several Complex Variables, AMS - CBMS Lectures, 1996.
- Morosawa, Nishimura, Taniguchi and Ueda, Holomorphic Dynamics, Cambridge University Press, 2002
- Barth, Peters and van de Ven, Compact Complex Surfaces, Springer-Verlag, 1984
- G. van der Geer, Hilbert modular surfaces, Springer-Verlag, 1987
- J. E. Humphreys, Reflection Groups and Coxeter Groups, Cambridge University Press, 1990
- S. Tabachnikov, Billiards , Soc. Math. France, 1995
- M. B. Bekka and M. Mayer, Ergodic theory and topological dynamics of group actions on homogeneous spaces, Cambridge University Press, 2000
Other useful references
- Doyle, Elkies, Gross, McMullen: Various papers
- Ghys, Dynamique des flots unipotents sur les espaces homogènes, Sem. Bourbaki 1991/92; Asterisque 206
- Hubbard and Papadopol, Superattractive fixed-points in Cn , Indiana Univ. Math. J. 43 (1994), 321-365.
- Briend and Duval, Deux caractérisations de la mesure d'équilibre d'un endomorphisme de Pk(C) , Publ. Math. IHES 93 (2001), 145-159.
- Masur and Tabachnikov, Rational billiards and flat structures
Prerequisites.
Intended for advanced graduate students.
Topics may include:
- Rational maps with icosahedral symmetry
- Solving quintic polynomials
- Currents and cohomology
- Dynamics of endomorphisms of Pn
- Dynamics on K3 surfaces
- Unimodular lattices
- Coxeter groups
- Salem numbers
- Unipotent flows on homogeneous spaces
- Ratner's theorem
- Gaps in Sqrt[n] mod 1
- Moduli of Riemann surfaces
- Teichmüller geodesic flow
- Billiards
- Hilbert modular surfaces
- Teichmüller curves
Calendar.
- Thu, 30 Jan. First class
- M-F, 22-30 Mar. Spring recess.
- Thu, 1 May. Last class